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Proof step 20 from proof inv-add-gnds (previous step)

err = ESUCCESS ↔ # lax = # gndx, ginval = ginval1, ginval0 = ginval2, gstore = gstore1[pstate.lnum, gstore1[pstate.lnum].gndlist:= (gstore1[pstate.lnum].gndlist + prefixn(# lax, gndx))] [pstate.lnum, gstore1[pstate.lnum, gstore1[pstate.lnum].gndlist:= (gstore1[pstate.lnum].gndlist + prefixn(# lax, gndx))][pstate.lnum] .ladrlist:= ( gstore1[pstate.lnum, gstore1[pstate.lnum].gndlist:= (gstore1[pstate.lnum].gndlist + prefixn(# lax, gndx))][pstate.lnum].ladrlist + lax) ], istore = istore1, istore0 = istore2, pstate = journal(nx.last), remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval2 = ∅, dom gstore0 ∪ elems nx = dom gstore1 ∪ ginval2, inv(gstore1[nx.last]), inv(istore1), inv(istore2), inv(gstore0), inv(gstore1 \ ginval2), inv-flashsize(prefixn(# lax, gndx), lax), pstate.lnum ∈ gstore1, pstate.lnum ∈ gstore1[pstate.lnum, gstore1[pstate.lnum].gndlist:= (gstore1[pstate.lnum].gndlist + prefixn(# lax, gndx))], nx.last ∈ gstore1, # lax ≤ # gndx, istore1 ⊑ istore2, pstate.index? ∨ pstate.journal?, ⌊err⌋ ∨ err = ESUCCESS ⊦ err = ESUCCESS, nx = [], dups(nx), dups(gstore1[pstate.lnum].ladrlist + lax), inv(gstore \ ginval2) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval2 ∧ (readonly.journal? → readonly.lnum = nx.last ∧ readonly.lnum ∈ gstore) ∧ (readonly.index? → readonly.lnum ∈ istore2) ∧ (readonly = unbuffered → syn)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
remove-refsize0(istore1) = istore1, remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval2 = ∅, dom gstore0 ∪ elems nx = dom gstore1 ∪ ginval2, # lax < # gndx, inv(gstore1[nx.last]), inv(istore1), inv(istore2), inv(gstore0), inv(gstore1 \ ginval2), inv-flashsize(prefixn(# lax, gndx), lax), nx.last ∈ gstore1, istore1 ⊑ istore2, ⌊err⌋ ⊦ # lax = # gndx, gndx = [], nx = [], dups(lax), dups(gstore1[nx.last].ladrlist), dups(gstore1[nx.last].ladrlist + lax), dups(nx), inv((gstore1[nx.last].gndlist:= (gstore1[nx.last].gndlist + prefixn(# lax, gndx))).ladrlist:= (gstore1[nx.last].ladrlist + lax)), nx.last ∈ ginval2

Rule argument

Additional information

Used simplifier rules: ⊦ # gndx = 0 ↔ gndx = []; (s)%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]%a: ⊦ ¬ dups(lax + lax0) → ¬ dups(lax) ∧ ¬ dups(lax0); (forward) from specification list-dup[laddress-list]%fwd-inv-loghead: ⊦ nx ≠ [] ∧ inv(gstore \ ginval) ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → inv(gstore[nx.last]); (forward) from specification apersistence-base%fwd-in-gstore-loghead: ⊦ nx ≠ [] ∧ ginval ∩ elems nx = ∅ ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval → nx.last ∈ gstore; (forward) from specification apersistence-base%unc: ⊦ ns ∪ ns0 = ns0 ∪ ns; from specification set-union[nat-set]%una: ⊦ (ns ∪ ns0) ∪ ns1 = ns ∪ ns0 ∪ ns1; from specification set-union[nat-set]%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%⊦ inv(gstore \ ns) → (inv(gstore[n, gblock] \ ns) ↔ n ∈ ns ∨ inv(gblock)); (ws)% ⊦ unbuffered ≠ readonly; (s)% ⊦ ¬ readonly.index?; (s)% ⊦ ¬ readonly.journal?; (s)% ⊦ n ∈ gstore → dom gstore ++ n = dom gstore; (s)% ⊦ dom gstore[n, gblock] = dom gstore ++ n; (s)% ⊦ gstore[n, gblock][n, gblock0] = gstore[n, gblock0]; (s)% ⊦ (gblock.gndlist:= gndx).ladrlist = gblock.ladrlist; (s)% ⊦ gstore[n, gblock][n] = gblock; (s)% ⊦ journal(m).journal?; (s)% ⊦ ¬ journal(m).index?; (s)% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)% ⊦ n ∈ gstore[n, gblock]; (s)% ⊦ journal(m).lnum = m; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)